00:02
The scores on an entrance exam are normally distributed about a center of 553 .9 and a standard deviation of 28 .7.
00:12
So what's the probability of randomly selecting one student and having their test score be 557 or higher? so i've shown this in the picture, and i want to figure out the area underneath the curve to the right of 557.
00:26
So to do that, we're going to figure out a z score for 557 by doing 557.
00:32
Minus the mean divided by the standard deviation.
00:44
And that's going to give us a z score of 0 .11.
00:49
And then we're going to look up in the standard normal probability table, a z score of 0 .11, and that corresponds to an area to the left of that z score being 0 .5338.
01:04
So to find the area to the right, we're going to have to do 1 minus 0 .5 .5.
01:10
Which is equal to 0 .4562.
01:19
So there's about a 45 .62 % chance of randomly picking a student and having their entrance score be higher than 557.
01:30
Now for the remainder of the question, now we're taking 255 students and finding their average.
01:37
So we're using the clt here, which says that the mean of the sampling distribution is going to be equal to the mean of the population...